What is the minimum value of $5x^2-20x+1357$?
Solution: Let $y=5x^2 -20x + 1357$.  First, complete the square as follows: $y=5x^2-20x+1357=5(x^2-4x)+1357$. To complete the square, we need to add $\left(\dfrac{4}{2}\right)^2=4$ after the $-4x$. So we have $y+20=5\left(x^2-4x+4\right)+1357$. This gives $y=5\left(x-2\right)^2+1337$.

Now, since $\left(x-2\right)^2\ge0$, the minimum value is when the squared term is equal to $0$.  So the minimum value is $y=5\left(x-2\right)^2+1337=5\cdot0+1337=\boxed{1337}$.